Monday, 18 May 2015

Which Strategy is Better? - Measuring Elapsed Years

Lead In:

Suppose you're reading a website and it explains that WWII began in 1939.
What different strategies could we mentally use to work out how many years ago that was?
Children volunteered to come out and show us the strategy they would do in their minds. (see pic)
We found out most of us have a preference for starting at the year in history and measure 'upwards' to the present year. A few of us though prefered to start at 2015 and subtract backwards. When asked why we thought that is less popular, some suggested it might be because we are stronger at adding mentally than subtracting. We also looked at the strategies shared and talked a bit about finding 'friendly' numbers to make life easier. 1950 was a a good example of a 'friendly' number to jump too.

Investigation: Is there a better strategy to use mentally?

Some years were displayed on the data screen in two columns: some a bit easier and some a bit more challenging.

Easier: How long ago was:

° 1935 ° 1965 ° 1924 ° 1895 ° 1845 ° 1942

In how many years will it be: ° 2060 ° 2100

More Challenging: How long ago was:

° 1933 ° 1977 ° 1865 ° 1845 ° 1845 ° 1755

In what year will you be ° 50 years old ° 85 years olds

Using mini-whiteboards and in pairs, they chose a year to measure how long ago it was.Partner A explained to Partner B the strategy they would use mentally to work out. Partner B needed to listen and write down what Partner A was explaining to them. Then, on their other whiteboard, Partner B explained to Partner A how to measure how long ago that same year was, but using a different strategy. The idea behind this was they would explore two different mental strategies to solve the same question. After they explored the two strategies, they then determined which they felt was easier and more effective for that particular year. Then, they repeated for another year displayed.

This pair explored whether it is easier to start back and move to the present OR start at 2015 and move back.

This pair also explored whether it is easier to move forwards or backwards along the number line and they experimented with using 1940 as a 'friendly' number to help solve mentally.

This pair were curious about an earlier strategy shared at the beginning of our inquiry and thought they would give it a try. Afterwards, they discussed their difference in preference. One girl explained that she doesn't like mentally seeing numbers visually on a number line and prefers to see them calculated like we do sometimes on pen and paper. Interesting......

Reflecting:

Afterwards, we regrouped together as a class and discussed:° Did we discover any new strategies that we might find useful?° Did we discover any strategies that might not be so useful when mentally working them out?° Did anyone's initial preference change regarding starting at the year or starting at 2015?